U.S. patent application number 14/662320 was filed with the patent office on 2016-09-22 for system for predicting amount of production and method for predicting amount of production.
The applicant listed for this patent is Hitachi, Ltd.. Invention is credited to Umeshwar DAYAL, Shouchun PENG, Anshuman SAHU, Iwao TANUMA, Ravigopal VENNELAKANTI, Masami YAMASAKI, Hiroshi YOSHIKAWA.
Application Number | 20160273314 14/662320 |
Document ID | / |
Family ID | 56924744 |
Filed Date | 2016-09-22 |
United States Patent
Application |
20160273314 |
Kind Code |
A1 |
TANUMA; Iwao ; et
al. |
September 22, 2016 |
SYSTEM FOR PREDICTING AMOUNT OF PRODUCTION AND METHOD FOR
PREDICTING AMOUNT OF PRODUCTION
Abstract
Provided is a production amount prediction system including: a
storage unit which stores a production amount prediction model
which is based on resources information including a resources
amount obtained in a previously drilled wellbore and a resources
recovery probability in the vicinity thereof; an input unit which
receives a trajectory coordinate of a planned wellbore as an input;
a production amount prediction unit which calculates a production
amount of the planned wellbore based on the production amount
prediction model by using a degree of influence of the previous
wellbore on the planned wellbore as at least one parameter; and a
display unit which displays the production amount of resources of
the planned wellbore calculated by the production amount prediction
unit.
Inventors: |
TANUMA; Iwao; (Tokyo,
JP) ; PENG; Shouchun; (Tokyo, JP) ; YOSHIKAWA;
Hiroshi; (Tokyo, JP) ; YAMASAKI; Masami;
(Tokyo, JP) ; DAYAL; Umeshwar; (Santa Clara,
CA) ; VENNELAKANTI; Ravigopal; (Santa Clara, CA)
; SAHU; Anshuman; (Santa Clara, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Hitachi, Ltd. |
Tokyo |
|
JP |
|
|
Family ID: |
56924744 |
Appl. No.: |
14/662320 |
Filed: |
March 19, 2015 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06Q 50/02 20130101;
G06N 20/00 20190101; G06N 7/005 20130101; G06Q 10/067 20130101;
E21B 43/00 20130101 |
International
Class: |
E21B 41/00 20060101
E21B041/00; G06N 99/00 20060101 G06N099/00; G06N 7/00 20060101
G06N007/00; G06Q 50/02 20060101 G06Q050/02; G06Q 10/06 20060101
G06Q010/06 |
Claims
1. A system for predicting amount of production comprising: a
storage unit which stores a model for predicting amount of
production which is based on resources information including an
amount of resources obtained in a previously drilled wellbore and a
resources recovery probability in the vicinity thereof; an input
unit which receives a coordinate of trajectory of a planned
wellbore as an input; a production amount prediction unit which
calculates a production amount of the planned wellbore based on the
model for predicting amount of production and the coordinate of
trajectory by using a degree of influence of the previous wellbore
on the planned wellbore as at least one parameter; and a display
unit which displays the production amount of resources of the
planned wellbore calculated by the production amount prediction
unit.
2. The system for predicting amount of production according to
claim 1, wherein the production amount prediction unit calculates
the degree of influence based on a positional relationship between
a trajectory coordinate of the planned wellbore and a trajectory
coordinate of the previous wellbore.
3. The system for predicting amount of production according to
claim 2, wherein, when a trajectory coordinate of a second planned
wellbore which is planned to be newly drilled is input to the input
unit, the production amount prediction unit calculates the degree
of influence among the wellbores based on a positional relationship
among the trajectory coordinate of the second planned wellbore, the
trajectory coordinate of the just-before input planned wellbore,
and the trajectory coordinate of the previous wellbore and
calculates the production amount of the resources of the second
planned wellbore.
4. A system for predicting amount of production comprising: a
storage unit which stores a model for predicting amount of
production which is based on resources information including an
amount of resources obtained in a previously drilled wellbore and a
resources recovery probability in the vicinity thereof; an input
unit which receives coordinates of trajectory of a plurality of
planned wellbores as an input; a production amount prediction unit
which calculates production amounts of resources of the planned
wellbores based on the model for predicting amount of production
and the coordinate of trajectory by using a degree of influence of
the previous wellbore on the planned wellbores as at least one
parameter; and a display unit which displays the production amounts
of resources of the planned wellbores calculated by the production
amount prediction unit.
5. The system for predicting amount of production according to
claim 4, further comprising: a plan constraint database which
stores constraints which a trajectory coordinate of a newly planned
wellbore is to satisfy; and a plan searching function which outputs
a plurality of candidates of a trajectory coordinate of the
wellbore which satisfies the constraints stored in the plan
constraint database in the vicinity of the trajectory coordinates
of the planned wellbores, wherein the display unit displays
production amount predicted values for the candidates in
parallel.
6. A method for predicting amount of production comprising: in a
display unit, storing a model for predicting amount of production
which is based on resources information including a resources
amount obtained in a previously drilled wellbore and a resources
recovery probability in the vicinity thereof, in advance; in an
input unit, receiving a coordinate of trajectory of a planned
wellbore as an input; in a production amount prediction unit,
calculating a production amount of the planned wellbore based on
the model for predicting amount of production and the coordinate of
trajectory by using a degree of influence of the previous wellbore
on the planned wellbore as at least one parameter; and in the
display unit, displaying the production amount of resources of the
planned wellbore calculated by the production amount prediction
unit.
7. The method for predicting amount of production according to
claim 6, wherein the production amount prediction unit calculates
the degree of influence based on a positional relationship between
a trajectory coordinate of the planned wellbore and a trajectory
coordinate of the previous wellbore.
8. The method for predicting amount of production according to
claim 7, wherein, in the case where a coordinate of trajectory of a
second planned wellbore which is planned to be newly drilled is
input to the input unit, the production amount prediction unit
calculates the degree of influence among the wellbores based on a
positional relationship among the trajectory coordinate of the
second planned wellbore, the trajectory coordinate of the
just-before input planned wellbore, and the trajectory coordinate
of the previous wellbore and calculates the production amount of
the resources of the second planned wellbore.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a system for predicting
amount of production and a method for predicting amount of
production for a wellbore of resources extraction applications.
[0003] 2. Description of the Related Art
[0004] As a background art, there is a technique disclosed in
US-2010/0185427-A. US-2010/0185427-A discloses a technique for
making a development plan for oil or gas by using geological
stratum data and the like. US-2010/0185427-A discloses a technique
for predicting a total production amount of oil or gas as a 3D
object based on distribution information of the oil or gas to make
a development plan.
SUMMARY OF THE INVENTION
[0005] In a technique disclosed in US-2010/0185427-A, a total
production amount of each wellbore is independently predicted and
calculated.
[0006] However, since resources included in the same land are
produced by extrusion into each wellbore, the production amounts of
the wellbore influence each other according to the interval between
the wellbores. Therefore, a technique for predicting amount of
production by considering the influence to make a drilling plan is
required.
[0007] There is disclosed a production amount prediction system
including: a storage unit which stores a production amount
prediction model which is based on resources information including
a resources amount obtained in a previously drilled wellbore and a
resources recovery probability in the vicinity thereof; an input
unit which receives a coordinate of trajectory of a planned
wellbore as an input; a production amount prediction unit which
calculates a production amount of the planned wellbore based on the
production amount prediction model by using a degree of influence
of the previous wellbore on the input planned wellbore as at least
one parameter; and a display unit which displays the production
amount of resources of the planned wellbore calculated by the
production amount prediction unit.
[0008] It is possible to make a drilling plan with a good recovery
efficiency of an amount of production by predicting the amount of
production by considering influence between wellbores.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 is a diagram illustrating a system configuration
according to an embodiment;
[0010] FIG. 2A is a diagram illustrating a record structure of a
production model database and a planned wellbore production model
database in the embodiment;
[0011] FIG. 2B is a diagram illustrating a record structure of a
database for wellbore trajectory in the embodiment;
[0012] FIG. 2C is a diagram illustrating a record structure of a
hydraulic fracturing history database and a hydraulic fracturing
plan database in the embodiment;
[0013] FIG. 2D is a diagram illustrating a record structure of a
fracturing state database in the embodiment;
[0014] FIG. 2E is a diagram illustrating a record structure of
history database for amount of production in the embodiment;
[0015] FIG. 2F is a diagram illustrating a recording structure of a
database for resources distribution according to the
embodiment;
[0016] FIG. 2G is a diagram illustrating a record structure of a
database of probability of recovering resources and a database of
probability of recovering planned resources in the embodiment;
[0017] FIG. 2H is a diagram illustrating a record structure of a
planned wellbore database in the embodiment;
[0018] FIG. 3 is a diagram illustrating an example of a mixture of
Gaussian distributions of a model for probability of recovering
resources according to the embodiment;
[0019] FIG. 4 is a diagram illustrating an example of data
representing a resources distribution in the embodiment;
[0020] FIG. 5 is a flowchart illustrating the entire processes of a
system for predicting amount of production according to the
embodiment;
[0021] FIG. 6 is a diagram illustrating an example of a correlation
between a fracturing water pressure and a variance in the
embodiment;
[0022] FIG. 7A is a diagram illustrating an example of a
correlation between a wellbore depth and an amount of limit for
recovering resources in the embodiment;
[0023] FIG. 7B is a diagram illustrating an example of a
correlation between a length of a wellbore horizontal portion and a
conversion coefficient of amount of production in the
embodiment;
[0024] FIG. 8 is a flowchart illustrating an amount of production
predicted value updating calculation procedure in the embodiment;
and
[0025] FIG. 9 is a diagram illustrating an example of a screen
displayed by a visualization function in the embodiment.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0026] Hereinafter, embodiments of the present invention will be
described in detail with reference to the drawings.
[0027] FIG. 1 is a diagram illustrating an example of a network
configuration including a system for predicting amount of
production 100 according to an embodiment. The system for
predicting amount of production 100 illustrated in FIG. 1 is a
computer system which enables production amount prediction by
considering interference of recovery efficiency between wellbores
by estimating an amount of production of each wellbore based on a
mathematical model where the wellbores share resources.
[0028] The system for predicting amount of production 100 is
connected to a network 180 and is capable of communicating data
with a client terminal 190. The client terminal 190 accesses the
system for predicting amount of production 100 and performs various
process of receiving data input from a wellbore developing planning
person and a wellbore manager and a process of displaying data
obtained from the system for predicting amount of production 100 on
a display or the like by using an input interface such as a
keyboard or a mouse.
[0029] The system for predicting amount of production 100 is
configured to include, as hardware components, a storage device 115
configured with a nonvolatile storage device such as a hard disk
drive, a memory 113 configured with a volatile storage device such
as a RAM, a CPU 114 (calculation device) which reads out a program
stored in the storage device 115 to the memory 113 to execute the
program, performs overall control of the system itself, and
performs a preliminary control process of various determinations
and calculations, and a communication device 112 which connects the
system for predicting amount of production 100 to the network 180
to perform a process of communicating with other devices.
[0030] The above-described program describes various functions of a
function for learning model of recovery 1231, a function for
learning model of production 123, a function for estimating model
planned recovery 1241, a function for interpolationing model of
production 124, a function for estimating amount of production 125,
a function of visualization 126, and a plan searching function
127.
[0031] The hard disk drive 115 includes a database of production
model 131, a database of wellbore trajectory 132, a database of
history of hydraulic fracturing 133, a database for fracturing
state 134, a database of history for amount of production 141, a
database for distributing resources 142, a database of probability
for recovering resources 143, a database of model of production
planned wellbore 151, a database of trajectory planned wellbore
152, a database of hydraulic fracturing plan 153, a database of
predicted value for amount of production 161, a database of
probability for recovering planned resources 162, a database for
constraint of plan 163, and a database of a planned wellbore 171,
and these database are referred to by a client terminal 190 through
the above-described program.
[0032] In addition, in the embodiment, although it is assumed that
the data input and output are performed by the client terminal 190,
the system for predicting amount of production 100 may have the
input and output functions and have devices (a display, a keyboard,
and the like), or a plurality of the client terminals 190 may be
connected through the network 180.
[0033] FIG. 5 is a flowchart illustrating whole processes of the
system for predicting amount of production 100 according to the
embodiment. A production amount prediction model which is based on
resources information including a resources amount obtained in a
previously drilled wellbore and a resources recovery probability in
the vicinity thereof is stored in the storage unit (the database of
production model 131, the database of probability for recovering
resources 143, and the database of history for amount of production
141).
[0034] An input unit (not shown) receives a coordinate of
trajectory of a planned wellbore as an input (S501).
[0035] The production amount prediction unit (function for
estimating amount of production 125) calculates a production amount
of the planned wellbore based on the production amount prediction
model by using a degree of influence of the previous wellbore on
the input planned wellbore as at least one parameter (S502). The
degree of influence will be described in detail in the description
of (Mathematical Formula 5).
[0036] In addition, the production amount prediction unit
calculates the degree of influence based on a positional
relationship between a coordinate of trajectory of the planned
wellbore and a coordinate of trajectory of the previous wellbore.
In the case where a coordinate of trajectory of a second planned
wellbore which is planned to be newly drilled is input to the input
unit, the production amount prediction unit calculates the degree
of influence among the wellbores based on a positional relationship
among the coordinate of trajectory of the second planned wellbore,
the coordinate of trajectory of the just-before input planned
wellbore, and the coordinate of trajectory of the previous wellbore
and calculates the production amount of the resources of the second
planned wellbore.
[0037] The display unit (function of visualization 126) displays
the production amount of resources of the planned wellbore
calculated by the production amount prediction unit (S503).
[0038] In addition, in the case of predicting the production
amounts of a plurality of the planned wellbores (newly planned
wellbores), the following processes are performed.
[0039] The input unit receives coordinates of trajectory of the
planned wellbores which are being planned as an input (S501).
[0040] The production amount prediction unit calculates the
production amounts of the resources of the planned wellbores based
on the production amount prediction model by using a degree of
influence of the previous wellbore on the planned wellbores as at
least one parameter (S502).
[0041] The display unit displays the production amounts of
resources of the planned wellbores calculated by the production
amount prediction unit (S503).
[0042] The plan constraint database (the database for constraint of
plan 163) stores constraints which the coordinate of trajectory of
the newly planned wellbore needs to satisfy. When the coordinate of
trajectory of the planned wellbore is input, the plan searching
function 127 outputs a plurality of candidates of the coordinate of
trajectory of the wellbore satisfying the constraints stored in the
plan constraint database in the vicinity of the input coordinate of
trajectory, and the display unit displays production amount
predicted values for the candidates in parallel. At this time, in
cooperation with an external wellbore drilling cost simulation
program, the plan searching function 127 may receive data of
drilling cost for the candidates from the program and display the
cost data of the candidates. Subsequently, data stored in the
database used by the system for predicting amount of production 100
according to the embodiment will be described.
[0043] The database of production model 131 is a database which is
configured with records having, as data fields, wellbore ID,
production starting date, and parameters (a limited resources
amount C.sub.i and a production coefficient K.sub.i) involved in
productivity of each wellbore. Initial values of the parameters
involved in the productivity are blank and are calculated and set
by the function for learning model of production 123. FIG. 2A
illustrates a record structure of the database of production model
131.
[0044] The database of wellbore trajectory 132 is a database which
stores wellbore trajectory coordinates of drilled wellbores and is
configured with records having, as data fields, wellbore ID and
wellbore trajectory data. The wellbore coordinate of trajectory is
3D coordinate information showing a position of a drill acquired
from sensor data during wellbore drilling, and the wellbore
trajectory data are configured with an array of wellbore
coordinates of trajectory. The initial values of the wellbore
trajectory data are blank and are calculated and set by the
function for learning model of production 123. FIG. 2B illustrates
a record structure of the database of wellbore trajectory 132.
[0045] The database of history of hydraulic fracturing 133 is a
database which is configured with records having, as data fields,
wellbore ID, the number of hydraulic fracturing stages, a
fracturing starting point coordinate of each fracturing stage, and
fracturing water pressure. The initial values of the parameters
involved in the fracturing are blank and are calculated and set by
the function for learning model of production 123. FIG. 2C
illustrates a record structure of the database of history of
hydraulic fracturing 133.
[0046] The database for fracturing state 134 is a database which is
configured with records having, as data fields, wellbore ID and
arrays of the number of subterranean fracture occurring locations
occurring at each stage number, a 3D coordinate of actual fracture
occurring location in each stage, and a fracture scale of the
location, wherein the number of arrays arranged is the number of
stages. The initial values of the parameters involved in the
fracturing are blank and are calculated and set by the function for
learning model of production 123. FIG. 2D illustrates a record
structure of the database for fracturing state 134. The fracture
location and the fracture scale in each stage are values obtained
by a micro-seismic analysis which is developed for a wellbore
development process for shale oil developing and which records and
analyzes seismic waves generated from the fracture location
occurring during hydraulic fracturing.
[0047] The database of history for amount of production 141 is a
database which is configured with records storing, as data fields,
wellbore ID and production month and year, the number of production
days per month, and monthly production amount with respect to the
wellbore having the wellbore ID from the production starting month
to the production ending month or the current date. The initial
values of the parameters involved in the productivity are blank and
are calculated and set by the function for learning model of
production 123. FIG. 2E illustrates a record structure of the
production amount database.
[0048] The database for distributing resources 142 is a database
which stores subterranean resources distribution information of a
wellbore development area. As illustrated in FIG. 4, an
subterranean resources distribution area 311 is expressed by a set
of rectangular parallelepiped blocks 321 having a predetermined
size. The block having a volume V.sub.n is defined as a rectangular
parallelepiped block with two diagonal vertices, a block ID (for
example, n) is allocated to the block, and an amount of resources
existing in the block area is defined as Pn. The initial values of
the parameters involved in the block are blank and are calculated
and set by the function for learning model of production 123. FIG.
2F illustrates a record structure of the database for distributing
resources 142. The record has, as data fields, the block ID, two
vertices defining the block area, and the resources amount in the
block.
[0049] FIG. 3 illustrates a resources recovery probability model.
In the resources recovery probability model, a probability of
absorption of oil resources from a periphery of a fracture
occurring in each hydraulic fracturing stage along a wellbore
trajectory of a wellbore 300 is approximated by a Gaussian
distribution, and the resources recovery probability model is
expressed by a mixture of Gaussian distributions 301 to 305 in the
hydraulic fracturing stages.
[0050] The database of probability for recovering resources 143 is
a database which stores, as records, parameters of elementary
Gaussian distributions constituting the mixture of Gaussian
distributions and a mixing ratio thereof. The initial values of the
parameters involved in each stage are blank and are calculated and
set by the function for learning model of production 123. FIG. 2G
illustrates a record structure of the database of probability for
recovering resources 143. The record has a database in which
wellbore ID(i), parameters (distribution center position
.mu..sub.ij, variance-covariance matrix A.sub.ij) of the Gaussian
distribution in each hydraulic fracturing stage (j) performed on
the wellbore, and a relative weighted value (w.sub.ij) which is the
mixing ratio of the Gaussian distribution to the mixture of
Gaussian distributions are arranged in the number of hydraulic
fracturing stages. The resources recovery probability distribution
occurring at the hydraulic fracturing stage j on the wellbore of
which the wellbore ID is i is expressed by the following Gaussian
distribution by using the parameters of the Gaussian distribution
stored in the database of probability for recovering resources
143.
[ Mathematical Formula 1 ] Pr i ( x , y , z , j i , j , ( A i , j )
, w i , j ) = j w i , j 1 ( 2 .pi. ) 3 / 2 A i , j 1 / 2 exp { - 1
2 ( r - i , j ) T A i , j - 1 ( r - i , j ) } in which , r = ( x ,
y , z ) ( Mathematical Formula 1 ) ##EQU00001##
[0051] The parameters of the mixture of Gaussian distributions are
generated by the function for learning model of production 123.
[0052] The database of model of production planned wellbore 151 is
a database which is configured with records having, as data fields,
wellbore ID, a scheduled production starting date, parameters
(limited resources amount C.sub.i and production coefficient
K.sub.i) involved in productivity of each wellbore. A group of the
parameters involved in the productivity is calculated and set by
the function for interpolationing model of production 124. The
database of model of production planned wellbore 151 is the same as
the record structure of the database of production model 131
illustrated in FIG. 2A.
[0053] The database of trajectory planned wellbore 152 is a
database which stores the wellbore coordinates of trajectory
obtained by the plan searching function 127 and is configured with
records having, as data fields, wellbore ID and wellbore trajectory
data. The wellbore trajectory data are configured with an array of
3D coordinates on the wellbore trajectory. The record structure of
the database of trajectory planned wellbore 152 is the same as the
record structure of the database of wellbore trajectory 132
illustrated in FIG. 2B.
[0054] The database of hydraulic fracturing plan 153 is a database
which stores planned values of the hydraulic fracturing for each
wellbore among the drilling plans stored in the database of
trajectory planned wellbore 152. The hydraulic fracturing plan
database is configured with records having, as data fields,
wellbore ID, the number of scheduled hydraulic fracturing stages, a
scheduled fracturing starting point coordinate in each fracturing
stage, and a planned value of fracturing water pressure, and the
record structure is the same as the record structure of the
database of history of hydraulic fracturing 133 illustrated in FIG.
2C.
[0055] The database of predicted value for amount of production 161
is a database which is configured with records having, as data
fields, wellbore ID and arrays of production month and year, and
the number of planned production days per month, and a monthly
production predicted value of the wellbore having the wellbore ID
from the scheduled production starting month to the scheduled
production ending month. The production amount predicted value is
generated by the function for estimating amount of production 125.
The record structure of the database of predicted value for amount
of production 161 is the same as the record structure of the
database of history for amount of production 141 illustrated in
FIG. 2E.
[0056] The database of probability for recovering planned resources
162 is a database which stores, as records, parameters of
elementary Gaussian distributions constituting the mixture of
Gaussian distributions and a mixing ratio thereof. The record
structure of the database of probability for recovering planned
resources 162 is the same as the record structure of the database
of probability for recovering resources 143 illustrated in FIG. 2G.
The parameters and the mixing ratio of the mixture of Gaussian
distributions are calculated and set by the function for
interpolationing model of production 124.
[0057] The database of a planned wellbore 171 is a database which
is configured with records having, as data fields, wellbore ID of a
wellbore which is planned to be developed and plan ID of a plan
which is to be performed on the wellbore, and the record structure
is illustrated in FIG. 2H.
[0058] The database for constraint of plan 163 stores constraint
conditions which need to be satisfied by drilling trajectories of
newly developed wellbores listed by the plan searching function
127. For example, the plan constraint database store a constraint
expression where a curvature of a trajectory has a certain value or
less because of the limitation of a drilling technique, a
constraint expression where the drilling direction of a horizontal
wellbore needs to be included in a predetermined range so that the
fracture locations are distributed to be dispersed vertically to
the wellbore depending on a distribution of subterranean stress, a
constraint expression where a certain depth range is specified so
that a horizontal wellbore passes through a shale layer in which
resources are intended to be extracted, a constraint expression
where a ground position for starting wellbore drilling is specified
by specifying a drill pad which is to be used, and the like.
[0059] Each function of the system for predicting amount of
production 100 according to the embodiment will be described. Each
function described hereinafter is operated by executing a program
included in the system for predicting amount of production 100.
[0060] The function for learning model of recovery 1231 is a
function of learning a resources recovery model. Namely, the
recovery model learning function is a function of writing data of
the fracture location and the fracture scale occurring due to the
hydraulic fracturing stored in the database for fracturing state
134 as an input and the parameters of the resources recovery
probability expressed by the mixture of Gaussian distributions as
an output in the database of probability for recovering resources
143.
[0061] The parameters of the resources recovery probability are
calculated as follows. A center estimated position .mu..sub.i,j of
the fracture occurring location is calculated according to the
following formula by using the coordinate (x.sub.i,j,k,
y.sub.i,j,k, z.sub.i,j,k) of the k-th fracture occurring location
corresponding to the hydraulic fracturing stage j of the wellbore
of which the wellbore ID is i stored in the database for fracturing
state 134 and the fracture scale w.sub.i,j,k at the fracture
occurring location.
[ Mathematical Formula 2 ] .mu. i , j = k w i , j , k ( x i , j , k
, y i , j , k , z i , j , k ) / k w i , j , k ( Mathematical
Formula 2 ) ##EQU00002##
[0062] The above formula is a calculation formula of the center
estimated position at the fracture occurring location.
[0063] In addition, a variance-covariance matrix A.sub.i,j is
calculated according to the following formula.
[ Mathematical Formula 3 ] ##EQU00003## ( Mathematical Formula 3 )
##EQU00003.2## A i , j = 1 k w i , j , k ( k w i , j , k ( x i , j
, k - .mu. i , j , 1 ) ( x i , j , k - .mu. i , j , 1 ) k w i , j ,
k ( x i , j , k - .mu. i , j , 1 ) ( y i , j , k - .mu. i , j , 2 )
k w i , j , k ( y i , j , k - .mu. i , j , 2 ) ( x i , j , k - .mu.
i , j , 1 ) k w i , j , k ( y i , j , k - .mu. i , j , 2 ) ( y i ,
j , k - .mu. i , j , 2 ) k w i , j , k ( z i , j , k - .mu. i , j ,
3 ) ( x i , j , k - .mu. i , j , 1 ) k w i , j , k ( z i , j , k -
.mu. i , j , 3 ) ( z i , j , k - .mu. i , j , 2 ) k w i , j , k ( x
i , j , k - .mu. i , j , 1 ) ( z i , j , k - .mu. i , j , 3 ) k w i
, j , k ( y i , j , k - .mu. i , j , 2 ) ( z i , j , k - .mu. i , j
, 3 ) k w i , j , k ( z i , j , k - .mu. i , j , 3 ) ( z i , j , k
- .mu. i , j , 3 ) ) ##EQU00003.3##
[0064] The above formula is a calculation formula of the
variance-covariance matrix representing the spread of the hydraulic
fracturing.
[0065] A weighted value w.sub.i,j for each hydraulic fracturing
stage representing the mixing ratio of the mixture of Gaussian
distributions is calculated according to the following formula.
[ Mathematical Formula 4 ] w i , j = k w i , j , k / j , k w i , j
, k ( Mathematical Formula 4 ) ##EQU00004##
[0066] The above formula is a calculation formula of the mixing
ratio of the mixture of Gaussian distributions.
[0067] The function for learning model of production 123 is a
function of writing the mixture of Gaussian distributions Pr.sub.i
representing (Mathematical Formula 1) calculated from the
parameters stored in the database of probability for recovering
resources 143, the resources distribution data P.sub.n stored in
the database for distributing resources 142, and the actual
achievement data U.sub.i,t of the production amount stored in the
database of history for amount of production 141 as an input and
the parameters of the production amount prediction formula as an
output in the database of production model 131. Herein, the index i
is set to the wellbore ID of interest, and the index t of the
actual achievement data of the production amount is set to the
index of time representing the production month.
[0068] It is assumed that the production amount U.sub.i,t, the
resources distribution P.sub.n, and the resources recovery
probability Pr.sub.i of the wellbore of which the wellbore ID is i
satisfy the following relational formula by using the resources
recovery limit amount C.sub.i and the production amount conversion
coefficient k.sub.i as the parameters of the production model.
[ Mathematical Formula 5 ] U i , t .apprxeq. n k i ( P n - .DELTA.
P n , t - C i ) j .intg. V n Pr i ( x , y , z , j .mu. i , j , A i
, j , w i , j ) x y z ( Mathematical Formula 5 ) ##EQU00005##
[0069] The above formula is a calculation formula of the production
amount.
[0070] The relational formula represents that large resources are
recovered from the subterranean location having large resources and
a high recovery probability. Herein, .DELTA..sub.n,t in the
relational formula of (Mathematical Formula 5) denotes a decrease
amount of resources of the volume V.sub.n of the subterranean
location n which is decreased by the resources produced from the
wellbore i before the production month t of interest as described
below.
[0071] In (Mathematical Formula 5), the predicted production amount
is calculated by calculating the production amount of each stage j
in the block n for each wellbore and calculating a sum thereof with
respect to the block (fracture location) and the hydraulic
fracturing stage (fracture scale) (corresponding to each E in
Mathematical Formula 5).
[0072] According to (Mathematical Formula 5), it can be understood
that the production amount in the block is proportional to an
integral value of the mixture of Gaussian distributions in the
block, the limited resources amount C.sub.i, and the production
coefficient K.sub.i. Among them, the integral value of the mixture
of Gaussian distributions is a parameter representing the degree of
influence of each block and denotes that, as the parameter becomes
large, the large resources are produced from the block. Namely, by
using the fracture location and the fracture scale as the
parameters of the mixture of Gaussian distributions, the degree of
influence between the wellbore can be expressed by the relative
weighted value (w.sub.ij).
[ Mathematical Formula 6 ] .DELTA. P n , t = i 1 k i ( t ' = 0 t -
1 U i , t j .intg. V n Pr i ( x , y , z , j .mu. i , j , A i , j ,
w i , j ) x y z ) ( Mathematical Formula 6 ) ##EQU00006##
[0073] The above formula is a calculation formula of the decreased
amount of the subterranean localized resources.
[0074] The parameters of the production model can be calculated by
a numerical method such as a least square method so that the error
is minimized when the relational formula of (Mathematical Formula
5) is satisfied by inserting data values of the database of
probability for recovering resources 143, the database for
distributing resources 142, the database of history for amount of
production 141, and the database of production model 131. By
representing the production amount in such as model, the phenomenon
that, since resources of a certain point are produced at the other
wellbore, the production amount of the other wellbore is decreased
can be understood.
[0075] The function for estimating model planned recovery 1241 is a
function of learning a recovery model for planned resources.
Namely, the function for estimating model planned recovery 1241 is
a function of writing the number of hydraulic fracturing stages,
the fracturing starting point coordinate of each fracturing stage,
and the fracturing pressure stored in the database of hydraulic
fracturing plan 153 as an input and the parameters of the planned
resources recovery probability expressed by using the mixture of
Gaussian distributions as an output in the database of probability
for recovering planned resources 162.
[0076] The parameters of the planned resources recovery probability
are calculated as follows. First, the center estimated position
.mu..sub.i,j of the fracture occurring location is defined as a
fracturing starting point coordinate value of the stage j of which
the wellbore ID stored in the database of hydraulic fracturing plan
153 is i. As described below, with respect to the
variance-covariance matrix A.sub.i,j, isotropy is assumed, and the
magnitude of the variance is denoted by .sigma..sup.2.sub.ij. Next,
a method of obtaining a size of the variance is described.
[ Mathematical Formula 7 ] A i , j = .sigma. i , j 2 ( 1 0 0 0 1 0
0 0 1 ) ( Mathematical Formula 7 ) ##EQU00007##
[0077] The above matrix is a variance-covariance matrix of the
planned resources recovery probability distribution.
[0078] FIG. 6 illustrates a scatter graph where the horizontal axis
denotes a fracturing pressure and the vertical axis denotes a
variance. In the graph, the fracturing water pressure stored in the
database of history of hydraulic fracturing 133 and the magnitude
of the variance-covariance matrix |A.sub.i,j|.sup.1/3 of the
mixture of Gaussian distributions stored in the database of
probability for recovering resources 143 representing the
distribution of the fracture locations occurring corresponding to
the fracturing are plotted. A linear relationship S601 which
approximates the relationship between the fracturing water pressure
and the variance is estimated by a least square method. A variance
value corresponding to the scheduled fracturing water pressure
value stored in the database of hydraulic fracturing plan 153 is
obtained by using the linear relationship S601, and the variance
value is defined as the variance .sigma..sup.2.sub.ij expressed in
the (Mathematical Formula 7), so that the variance-covariance
matrix of the mixture of Gaussian distributions stored in the
database of probability for recovering planned resources 162 is
estimated.
[0079] As described below, the relative weighted w.sub.i,j of the
probability distribution of the hydraulic fracturing stage j is set
to the relative ratio of the scheduled fracturing water pressure
value E.sub.i,j. In this manner, the parameters of the mixture of
Gaussian distributions stored in the database of probability for
recovering planned resources 162 are estimated.
[ Mathematical Formula 8 ] w i , j = E i , j k E i , k (
Mathematical Formula 8 ) ##EQU00008##
[0080] The above formula is a calculation formula of the mixing
ratio of the mixture of Gaussian distributions representing the
planned resources recovery probability distribution.
[0081] The function for interpolationing model of production 124 is
a function of writing the wellbore trajectory coordinates stored in
the database of trajectory planned wellbore 152 as an input and the
parameters of the production amount prediction formula as an output
in the database of model of production planned wellbore 151.
[0082] The parameters of the planned production model are
calculated as follows. The resources recovery limit amount C.sub.i
of the wellbore of which the wellbore ID is i is obtained from the
correlation between a wellbore depth of an existing wellbore and a
resources recovery limit amount of the wellbore. As illustrated in
FIG. 7A, a scatter graph of the wellbore depth of the existing
wellbore and the resources recovery limit amount of the wellbore is
plotted. A linear relationship S701 which is best approximate to
the correlation between the wellbore depth and the resources
recovery limit amount of the wellbore is estimated by using a least
square method. Subsequently, the wellbore depth of the wellbore i
which is being planned is obtained by referring to the database of
trajectory planned wellbore 152, and the resources recovery limit
amount C.sub.i of the corresponding wellbore is obtained by using
the linear relationship S701.
[0083] Next, the production amount conversion coefficient k.sub.i
is obtained from the correlation between a length of a wellbore
horizontal portion of the existing wellbore and a production amount
conversion coefficient of the wellbore. First, as illustrated in
FIG. 7B, a scatter graph between the length of the wellbore
horizontal portion of the existing wellbore and the production
amount conversion coefficient of the wellbore is plotted. A linear
relationship S702 which is best approximate to the correlation of
the scatter graph is estimated by using a least square method.
Subsequently, the length L.sub.i of the wellbore horizontal portion
of the wellbore i which is being planned is obtained by referring
to the database of trajectory planned wellbore 152, and the
production amount conversion coefficient of k.sub.i of the
corresponding wellbore is obtained by using the linear relationship
S702.
[0084] The function for estimating amount of production 125 is a
function of writing the parameters included in (Mathematical
Formula 5) and (Mathematical Formula 6) obtained by referring to
the database for distributing resources 142, the database of
probability for recovering resources 143, the database of
production model 131, the database of probability for recovering
planned resources 162, and the database of model of production
planned wellbore 151 as an input and the production amount
predicted value of a time t after the current time calculated by
using (Mathematical Formula 5) and (Mathematical Formula 6)
determining the parameter values as an output in the database of
predicted value for amount of production 161.
[0085] FIG. 8 illustrates a calculation procedure for estimating
the production amount predicted value up to a prediction time t
before the current time with respect to all the existing wellbore
and all the planned wellbores. First, the function for learning
model of recovery 1231 calculates the mixture of Gaussian
distributions of the resources recovery probability with respect to
all the existing wellbores and updates the database of probability
for recovering resources 143 (S801). Subsequently, the function for
learning model of production 123 calculates the production model
parameters with respect to all the existing wellbores and updates
the database of production model 131 (S802). Subsequently, the
function for estimating model planned recovery 1241 calculates the
mixture of Gaussian distributions of the resources recovery
probability with respect to all the planned wellbores and updates
the database of probability for recovering planned resources 162
(S803). Subsequently, the function for interpolationing model of
production 124 calculates the production model parameter with
respect to all the planned wellbores and updates the database of
model of production planned wellbore 151 (S804). Finally, the
function for estimating amount of production 125 calculates the
production amount predicted value up to the prediction time t with
respect to all the existing wellbores and all the planned
wellbores, updates the database of predicted value for amount of
production 161, and stores the production amount predicted value
estimation calculation (S805).
[0086] The calculation procedure for estimating the production
amount predicted value illustrated in FIG. 8 is performed by a
batch process planned by the client terminal 190, by an execution
request according to user's input, or by using the updating of the
database of wellbore trajectory 132, the database of history of
hydraulic fracturing 133, the database for fracturing state 134,
the database of history for amount of production 141, the database
for distributing resources 142, the database of trajectory planned
wellbore 152, the database of hydraulic fracturing plan 153, the
database for constraint of plan 163, or the database of a planned
wellbore 171 as a trigger.
[0087] The function of visualization 126 uses, as an input, the
data stored in the database of a planned wellbore 171, the database
of wellbore trajectory 132, the database of trajectory planned
wellbore 152, the database for distributing resources 142, the
database of history for amount of production 141, and the database
of predicted value for amount of production 161 and provides a
function of displaying the content of the data in a graphical
manner for the better understanding.
[0088] FIG. 9 illustrates an example of a screen displayed by the
function of visualization 126. The screen is configured to include
a plan ID selecting drop-down list S901, a wellbore trajectory
representing portion S902, a production amount graph S903, and an
evaluation index representing portion S904.
[0089] S901 is a drop-down list for selecting the plan ID. The plan
IDs included in the database of a planned wellbore 171 are listed,
and the user selects the plan ID, the wellbore trajectory, the
production amount, and the evaluation index of S902, S903, and S904
with respect to all the wellbore having the plan ID are
visualized.
[0090] S902 is a screen for identifying an overview of the wellbore
trajectory. S9021 is the trajectory of developed wellbore, and
S9022 is an example of the trajectory of the wellbore having the
plan ID selected from the plan ID selecting drop-down list S701.
With respect to the trajectory of the developed wellbore of S9021,
the trajectory coordinates are extracted by referring to the
database of wellbore trajectory 132 and the trajectory is
represented by a solid line, and with respect to the trajectory of
the development planned wellbore in the plan such as S9022, the
trajectory coordinates are extracted by referring to the database
of trajectory planned wellbore 152, and the trajectory is
represented by a broken line so that the trajectory can be
distinguished from the trajectory of the developed wellbore. In
addition, with respect to the plotted trajectories, the wellbore
IDs such as 1 for S9021 and 5 for S9022 are represented on the
screen. In addition, the resources content information at each 3D
subterranean position is extracted by referring to the database for
distributing resources 142, and the recourses content is
represented with gradation such as S9023 according to the resources
content information of each point so that it can be easy to
identify intuitively.
[0091] S903 is a screen for identifying the production amount
achievement and the predicted production amount for each wellbore.
The screen S903 is configured with a graph display portion S9031
and a wellbore ID corresponding display portion S9032. In the graph
display portion S9031, the vertical axis denotes a production
amount, and the horizontal axis denotes a time (month and year),
and the graph display portion displays a change in production
amount for each wellbore in each time, that is, the actual
achievement value of the production amount up to the current time
and the production amount predicted value after the current time.
The actual achievement value of the production amount is
represented for each wellbore by referring to the database of
history for amount of production 141. The production amount
predicted value is represented for each wellbore by referring to
the database of predicted value for amount of production 161. In
the ID corresponding display portion S9032, it is displayed by
using explanatory notes which of the wellbore IDs of the wellbore
the change in production amount corresponds to.
[0092] S904 is a screen of providing an evaluation index for each
plan. For example, in S9041, by referring to the production amount
of each wellbore included in the database of history for amount of
production 141 and the production amount predicted value of each
planned wellbore included in the database of predicted value for
amount of production 161 and adding the production amount and the
production amount predicted value, the predicted value of the sum
of the production amounts is displayed. In addition, in S9042, a
benefit predicted value is calculated by inserting the total
production amount calculated in S9041 into a benefit model formula,
and the benefit predicted value to be displayed.
[0093] Accordingly, in the course of drilling/development of the
wellbore, every time when new data input, change in plan, and
addition of a new plan occur, the user identifies the content by
using the screen of FIG. 9 so that the user can perform appropriate
job decision and business decision.
[0094] The plan searching function 127 is a function of receiving,
as an input, the constraint expression which the position
coordinate of the drilling trajectory of the newly planned wellbore
stored in the database for constraint of plan 163 needs to satisfy
and semi-automatically listing and displaying the candidates of the
drilling trajectory which satisfy the plural constraint
expressions. In the case of manually inputting the drilling
trajectory of the newly planned wellbore, the 3D coordinates of the
wellbore trajectory are input and simultaneously displayed on the
wellbore trajectory representing portion S902 in the display screen
of the function of visualization 126 by using client terminal 190.
At the input trajectory coordinates, the plural constraint
expressions stored in the database for constraint of plan 163 are
evaluated, and only in the case where the constraints are
satisfied, the inputting data are allowed, so that the storing in
the database of trajectory planned wellbore 152 is performed. In
the case of automatically generating the drilling trajectory of the
newly planned wellbore, according to a method such as constraint
programming where the constraint expressions stored in the database
for constraint of plan 163 are set as conditions, potential
drilling trajectory candidates which satisfy the constraints are
sequentially listed. The production amount predicted value is
automatically calculated based on the listed trajectories according
to the calculation procedure for the production amount predicted
value illustrated in the FIG. 8, and the information displayed in
the function of visualization 126 is updated.
* * * * *